Inverse Functions (Grade 12 NSC Matric Mathematics): Flashcards

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Inverse Functions
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What inverse function does

Reverses/undoes the original function

Formal condition: f−1(f(x))=f^{-1}(f(x)) = ?

xx

Requirement for invertible function

Must be one-to-one relation

Function with inverse is called

Invertible

Step 1 to find inverse

Interchange xx and yy

Steps 2-3 to find inverse

Make yy subject, express in function notation

ff and f−1f^{-1} graphs: reflections about line

y=xy = x

Inverse function notation

f−1(x)f^{-1}(x) (not an exponent)

Reciprocal function formula

1f(x)\frac{1}{f(x)}

When function has no inverse

Not one-to-one (fails horizontal line test)

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